Responding to the article, Facebook said it had wanted to show that Freedom From Facebook was "not simply a spontaneous grassroots campaign" and that the movement was "supported by a well-known critic of our company".

It said any suggestion that it had been an anti-Semitic attack was "reprehensible".

Chief executive Mark Zuckerberg later said that neither he nor chief operating officer Sheryl Sandberg had been "in the loop" about Definers' actions and added that Facebook would no longer work with the firm.

Sir Nick Clegg - the UK's former deputy prime minister who recently became Facebook's head of global policy - will oversee a review of the social network's use of other lobbyists and will report back on the matter to Ms Sandberg.

Did Facebook try to drag Google into its controversies?

After a New York Times article revealed that Facebook had undeclared deals with phone-makers to share user data with them, the company set up focus groups to test how it should react.

One approach it tested was arguing that Google had similar data-sharing deals with phone-makers.

When asked to testify in front of the Senate Intelligence Committee, Facebook lobbied for the hearing to include a Google representative, the newspaper said.

Google was asked to testify but did not show up. Many of the news headlines of the day focused on Google's empty chair.

What were the other allegations?

The report also said Facebook had urged staff to use only Android devices, after Apple's Tim Cook had criticised the social network.

Facebook said it encouraged employees and executives to use Android because "it is the most popular operating system in the world".

The newspaper also suggested Facebook had struggled to work out how to deal with a post made by Donald Trump in 2015, calling for a ban on Muslim immigration.

"To suggest that the internal debate around this particular case was different from other important free speech issues on Facebook is wrong," the company said in a blog post.

What has the reaction been?

The Wall Street Journal reported that morale at Facebook had fallen amid the ongoing scrutiny of the company.

It said it had seen an internal survey taken by 29,000 employees that reported only half were "optimistic" about the company's future, a fall of 32 percentage points from the previous year.

The Open Society Foundations president, Mr Gaspard, said Facebook had used tactics "out of Putin's playbook" that had "no place in an important debate about the integrity of our elections".

Democratic congressman David Cicilline said in a post that "Facebook cannot be trusted to regulate itself".

"Facebook executives will always put their massive profits ahead of the interests of their customers," he said.

"Congress should get to work enacting new laws to hold concentrated economic power to account."

Facebook said it had ended its relationship with Definers and had never hidden its work with the consultancy.

Definers has not yet responded to the BBC's request for comment.

Analysis

by Rory Cellan-Jones, technology correspondent

We knew that Facebook's handling of its recent crises had been inept.

Mark Zuckerberg's description of the idea that fake news put Donald Trump in the White House as "crazy" was a prime example.

But now the New York Times has painted a startling picture not just of negligence and mismanagement by Facebook's leaders but of deeply questionable tactics as they fought to protect the image of their company.

This new evidence of ethical failings will also embolden politicians and regulators around the world who want to clip Facebook's wings.